Details

Time bar (total: 25.8s)

sample72.0ms

Algorithm
intervals
Results
35.0ms256×body80valid
22.0ms256×pre80true

simplify318.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
317.0ms
(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 8.5b

localize32.0ms

Local error

Found 3 expressions with local error:

8.6b
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
0.3b
(* (/ b a) (/ b a))
0.0b
(- 1 (* (/ b a) (/ b a)))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
46×add-sqr-sqrt
40×times-frac
33×*-un-lft-identity
32×add-cube-cbrt
15×add-cbrt-cube add-exp-log
13×swap-sqr associate-*r* associate-*l*
11×pow1
5×add-log-exp
4×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv unswap-sqr
3×sqrt-prod insert-posit16
2×difference-of-squares
1×pow2 frac-times rem-sqrt-square sub-neg sqrt-pow1 pow-plus flip3-- pow1/2 diff-log pow-prod-down associate-*l/ associate-*r/ pow-sqr *-commutative pow-prod-up flip--
Counts
3 → 97
Calls
3 calls:
Slowest
24.0ms
(* (/ b a) (/ b a))
9.0ms
(- 1 (* (/ b a) (/ b a)))
2.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

series108.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
50.0ms
(- 1 (* (/ b a) (/ b a)))
35.0ms
(* (/ b a) (/ b a))
24.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

simplify4.3s

Counts
94 → 106
Calls
94 calls:
Slowest
422.0ms
(* (/ (* (cbrt b) (cbrt b)) (* (cbrt a) (cbrt a))) (/ (* (cbrt b) (cbrt b)) (* (cbrt a) (cbrt a))))
278.0ms
(/ (exp 1) (exp (* (/ b a) (/ b a))))
246.0ms
(* (* (* (/ b a) (/ b a)) (/ b a)) (* (* (/ b a) (/ b a)) (/ b a)))
190.0ms
(* (/ (* (* b b) b) (* (* a a) a)) (* (* (/ b a) (/ b a)) (/ b a)))
178.0ms
(* (/ (* (* b b) b) (* (* a a) a)) (/ (* (* b b) b) (* (* a a) a)))

prune988.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 8.5b

localize18.0ms

Local error

Found 4 expressions with local error:

8.6b
(sqrt (fabs (- 1 (/ (* b (/ b a)) a))))
6.4b
(/ (* b (/ b a)) a)
0.2b
(* b (/ b a))
0.0b
(- 1 (/ (* b (/ b a)) a))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt
18×*-un-lft-identity add-cbrt-cube add-exp-log
15×add-cube-cbrt
13×times-frac associate-*r*
7×pow1
6×add-log-exp
5×cbrt-undiv div-exp
4×prod-exp cbrt-unprod insert-posit16
3×associate-/r* associate-*l* sqrt-prod
2×associate-*r/ div-inv difference-of-squares unswap-sqr
1×rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 flip3-- pow1/2 diff-log pow-prod-down *-commutative flip-- associate-/l* distribute-lft-out-- associate-/l/
Counts
4 → 88
Calls
4 calls:
Slowest
19.0ms
(/ (* b (/ b a)) a)
11.0ms
(* b (/ b a))
6.0ms
(- 1 (/ (* b (/ b a)) a))
2.0ms
(sqrt (fabs (- 1 (/ (* b (/ b a)) a))))

series151.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
60.0ms
(- 1 (/ (* b (/ b a)) a))
44.0ms
(/ (* b (/ b a)) a)
31.0ms
(* b (/ b a))
16.0ms
(sqrt (fabs (- 1 (/ (* b (/ b a)) a))))

simplify3.5s

Counts
62 → 100
Calls
62 calls:
Slowest
497.0ms
(* (* (* b b) b) (/ (* (* b b) b) (* (* a a) a)))
286.0ms
(/ (* (* (* b b) b) (/ (* (* b b) b) (* (* a a) a))) (* (* a a) a))
263.0ms
(/ (* (* (* b (/ b a)) (* b (/ b a))) (* b (/ b a))) (* (* a a) a))
231.0ms
(* (* (* b b) b) (* (* (/ b a) (/ b a)) (/ b a)))
184.0ms
(/ (* (* (* b b) b) (* (* (/ b a) (/ b a)) (/ b a))) (* (* a a) a))

prune950.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 8.4b

localize42.0ms

Local error

Found 4 expressions with local error:

8.6b
(sqrt (fabs (- 1 (/ (* b (/ b a)) a))))
8.6b
(sqrt (fabs (- 1 (/ (* b (/ b a)) a))))
6.4b
(/ (* b (/ b a)) a)
6.4b
(/ (* b (/ b a)) a)

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
22×add-cbrt-cube add-exp-log
12×add-sqr-sqrt
10×*-un-lft-identity add-cube-cbrt
8×cbrt-undiv div-exp
6×pow1 associate-/r* times-frac sqrt-prod
4×prod-exp cbrt-unprod insert-posit16 add-log-exp
2×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 associate-*r/ div-inv associate-/l* associate-/l/
Counts
4 → 78
Calls
4 calls:
Slowest
11.0ms
(/ (* b (/ b a)) a)
10.0ms
(/ (* b (/ b a)) a)
1.0ms
(sqrt (fabs (- 1 (/ (* b (/ b a)) a))))
1.0ms
(sqrt (fabs (- 1 (/ (* b (/ b a)) a))))

series111.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
39.0ms
(/ (* b (/ b a)) a)
26.0ms
(/ (* b (/ b a)) a)
26.0ms
(sqrt (fabs (- 1 (/ (* b (/ b a)) a))))
20.0ms
(sqrt (fabs (- 1 (/ (* b (/ b a)) a))))

simplify4.0s

Counts
52 → 90
Calls
52 calls:
Slowest
572.0ms
(/ (* (* (* b b) b) (* (* (/ b a) (/ b a)) (/ b a))) (* (* a a) a))
227.0ms
(/ (* (* (* b b) b) (/ (* (* b b) b) (* (* a a) a))) (* (* a a) a))
226.0ms
(/ (* (* (* b b) b) (/ (* (* b b) b) (* (* a a) a))) (* (* a a) a))
224.0ms
(/ (* (* (* b (/ b a)) (* b (/ b a))) (* b (/ b a))) (* (* a a) a))
206.0ms
(/ (* (* (* b (/ b a)) (* b (/ b a))) (* b (/ b a))) (* (* a a) a))

prune1.3s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 8.4b

localize32.0ms

Local error

Found 4 expressions with local error:

9.4b
(* b (/ (/ b a) a))
8.6b
(sqrt (fabs (- 1 (* b (/ (/ b a) a)))))
0.2b
(/ (/ b a) a)
0.0b
(- 1 (* b (/ (/ b a) a)))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
144×times-frac
93×add-sqr-sqrt
83×*-un-lft-identity add-cube-cbrt
43×associate-*r*
18×add-cbrt-cube add-exp-log
13×associate-/l*
9×div-inv
7×pow1
6×cbrt-undiv div-exp add-log-exp
4×insert-posit16
3×associate-/r* associate-*l* prod-exp sqrt-prod cbrt-unprod unswap-sqr
1×rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 flip3-- pow1/2 diff-log pow-prod-down associate-*r/ *-commutative flip-- associate-/l/
Counts
4 → 164
Calls
4 calls:
Slowest
26.0ms
(* b (/ (/ b a) a))
7.0ms
(/ (/ b a) a)
4.0ms
(- 1 (* b (/ (/ b a) a)))
1.0ms
(sqrt (fabs (- 1 (* b (/ (/ b a) a)))))

series141.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
43.0ms
(/ (/ b a) a)
42.0ms
(- 1 (* b (/ (/ b a) a)))
35.0ms
(* b (/ (/ b a) a))
21.0ms
(sqrt (fabs (- 1 (* b (/ (/ b a) a)))))

simplify6.3s

Counts
171 → 176
Calls
171 calls:
Slowest
522.0ms
(* (* (* b b) b) (* (* (/ (/ b a) a) (/ (/ b a) a)) (/ (/ b a) a)))
353.0ms
(/ (/ (* (* b b) b) (* (* a a) a)) (* (* a a) a))
306.0ms
(/ (exp 1) (exp (* b (/ (/ b a) a))))
277.0ms
(/ (* (* (/ b a) (/ b a)) (/ b a)) (* (* a a) a))
210.0ms
(/ (/ (* (cbrt b) (cbrt b)) (* (cbrt a) (cbrt a))) (* (cbrt a) (cbrt a)))

prune1.8s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 8.4b

regimes134.0ms

Accuracy

0% (0.1b remaining)

Error of 7.5b against oracle of 7.4b and baseline of 7.5b

bsearch3.0ms

end0.0ms

sample1.3s

Algorithm
intervals
Results
900.0ms8000×body80valid
285.0ms8000×pre80true